Super Modified Combination Sum

Algebra Level 3

k=1504(4k1)(20154k1) \large\displaystyle \sum_{k=1}^{504} \left ( 4k-1 \right ) \binom{2015}{4k-1}

If the sum above can be written as p.qr p.q^{r} , where pp, qq and rr are positive integers with qq being a prime.

Evaluate p+q+r p+q+r .

Image Credit: Wikimedia TED-43.
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